3.15 Electrical, Optical, and Magnetic Materials and Devices
Caroline A. Ross
Fall Term, 2006
Problem Set #1
Semiconductor Fundamentals
Due Monday, September 18, 2005
Reference: Chapters 1-3 of Pierret.
1. Review of 3.024. Write a brief (1 line) definition for each of the following:
conduction & valence bands
band gap
effective mass
intrinsic & extrinsic semiconductors
dopant
donors & acceptors
n-type & p-type materials
n+ (or p+) material
majority & minority carriers
density of states
Fermi function
Fermi energy (or level)
degenerate semiconductor
extrinsic & intrinsic temperature regimes
freeze-out
drift velocity
thermal motion
drift current
mobility
resistivity or conductivity
diffusion
diffusion current
diffusion coefficient
recombination & generation
direct thermal R-G
photogeneration
steady state
equilibrium
minority carrier lifetime
minority carrier diffusion length
2. a) Draw sketches showing gc(E), gv(E), f(E) and the carrier distributions for a semiconductor
that is (i) intrinsic, (ii) n-type. (make the sketches with the E axis vertical.)
b) Germanium has the same crystal structure as silicon but its band gap is 0.67 eV.If the total
density of states in the conduction band (Nc) and in the valence band (Nv) are the same as
they are for silicon, what value of ni would you expect for Ge at 300K?
c) The Ge is now doped with B and with P. Both dopants have the same concentration. Assume
the B and P energy levels are each 40 meV from the band edge. If mn*/mp* = 0.01, draw
the band diagram of the doped Ge as accurately as you can, showing Eg, Ef and Ei.
3. a) What factors affect the mobility of a carrier? (2-3 sentences)
b) A piece of p-type Si with NA = 1018 cm-3 and a length of 1 cm is heated at one end. This affects
the value of ni as follows:
Hot
ni = 1012 cm-3
Cold
ni = 1010 cm-3
Consider only the electrons in the Si, neglecting the motion of the holes. Where do drift and
diffusion of the electrons occur? Estimate the electric field at the cold end of the Si.
4. Si and Ge can be mixed together to form a SixGe1-x semiconductor material. The band gap
increases linearly with x, from the value for pure Ge at x = 0 to the value for pure Si at x = 1.
You have a bar of intrinsic SiGe material, with x = 0.2 at one end and x = 0.8 at the other end.
The composition varies linearly with distance. Draw the equilibrium band structure in as much
detail as you can and explain whether there is any drift or diffusion or R&G taking place in the
material. (this should be a short answer)
5. Light is flashed onto the surface of a piece of intrinsic semiconductor very quickly, then the
light is turned off. Draw a sketch to show how the concentration of carriers varies with distance
into the semiconductor, at different times after the light is turned off. Give an expression that
describes this behavior (note – you do not have to solve this equation, just explain the various
terms). What determines the recombination rate?